Another source working on Puzder’s confirmation preparation also told Garrett that the odds were about 80 percent that the CKE Restaurants executive would pull out of the nomination.

The news comes after days of intense scrutiny over Puzder’s fitness to lead the Labor Department and questionable support from Republican senators.

Puzder, who previously led the company that owns fast food chains Carl’s Jr. and Hardee’s, came under fire earlier this month after reports that he and his wife had employed an undocumented immigrant for housework.

And Puzder’s past has also come under the microscope in recent days. Earlier this week, Politico unearthed a 1990 episode of “The Oprah Winfrey Show” where Puzder’s ex-wife, Lisa Fierstein, accused him of domestic abuse. Puzder has repeatedly denied the allegations and Fierstein recanted her accounts of abuse shortly after the episode aired.

Senior Senate GOP sources who were confident of Puzder’s nomination on Monday told Garrett they were now dialing back optimism, saying that there are serious “rumblings” about Republicans not backing Puzder and a very high probability Puzder will withdraw.

At least five Republicans in the Senate have not made public how they’ll vote on Puzder, CBS News’ John Nolen reports. Sens. Susan Collins of Maine, Johnny Isakson of Georgia, Lisa Murkowski of Alaska, Mike Enzi of Wyoming and Tim Scott of South Carolina -- all members of the Senate HELP committee -- have declined to state how they plan to vote until after Puzder’s hearing. (Most of the senators have indicated they don’t typically comment with their vote ahead of hearings.)

The White House declined to comment on the status of Puzder’s nomination.